"Based on the fraud committed by Senator Ted Cruz during the Iowa Caucus, either a new election should take place or Cruz results nullified," Trump tweeted Wednesday.

"Ted Cruz didn't win Iowa, he stole it," he wrote. "That is why all of the polls were so wrong and why he got far more votes than anticipated."

Cruz laughed off the accusations and said Trump is "losing it."

The inflammatory remarks marked a reversal for Trump, who on Monday night delivered a concession speech thanking Iowans for his second-place finish and congratulating Cruz. On Tuesday night in New Hampshire, he told reporters he was "very happy with what happened in Iowa."

But by Wednesday, Trump was laying out a list of accusations. He pointed to a mailer sent by the Cruz campaign headlined "voting violation" and resembled an official notice. The mailer showed recipients their history of voting or not in past caucuses, along with the turnout record of their neighbors, and drew complaints from Iowa's secretary of state.

Trump also called out Cruz backers for circulating a false rumor Monday night that Ben Carson was dropping out of the race as caucusing was under way.

"Many people voted for Cruz over Carson because of this Cruz fraud," Trump wrote, suggesting the efforts may have given Cruz a winning edge.

Iowa Rep. Steve King, a national co-chairman of Cruz's campaign, wrote on Twitter Monday evening: "Looks like (Carson) is out. … Skipping NH & SC is the equivalent of suspending. Too bad this information won't get to all caucus goers." Carson has called the comments "dirty tricks."

Cruz spokesman Rick Tyler told CNN on Wednesday that Cruz apologized personally to Carson for the mistake. He said the Cruz team "as a campaign" never alleged Carson was dropping out.

"It may be that some of the surrogates or some of our caucus precinct captains … went too far," Tyler told CNN. If so, he added, "that was in error, that was wrong."

Cruz said Trump simply can't stand to lose.

"Donald Trump guaranteed a victory in Iowa and then he lost," Cruz said. "And he doesn't like that. And his reaction is that he breaks down, he really has problems."

For his part Carson spoke of "deceptive Iowa caucus tactics," implying that he, too, was upset about the false claim about his departure from the race.

"It's clear that there were people who tried to take advantage of a situation," Carson said.

Trump's Twitter reaction to his Iowa showing strayed significantly from his public comments on several morning TV shows Wednesday and at a rally Tuesday night.

Asked about Cruz at a press conference before the rally, Trump said Cruz had insulted Carson and Iowans but would not say whether he thought the Texas senator had run a dirty campaign.

"I don't know, I can't tell you yet," he said.

But Trump campaign manager Corey Lewandowski was pointed on the matter Wednesday.

"What Sen. Cruz did to Ben Carson was a disgrace and an insult to Dr. Carson and the process," he said. "What Sen. Cruz did to the voters of Iowa was also a disgrace in regard to their phony voter violation form. Additionally, they misrepresented Mr. Trump and unfortunately this happens all the time with crooked politicians."

Asked whether the campaign planned to file a formal complaint, he said: "Wait and see."

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